The data set below shows the amount of trash generated by ten households (in pounds per day). Assume that the population is normally distributed.

Question

The data set below shows the amount of trash generated by ten households (in pounds per day). Assume that the population is normally distributed.

3.9   4.6   15.6   10.5   16.0   6.7   12.0   9.2   13.8 16.8

(a) Construct a 95% confidence interval for the mean based on the sample.

(b) Construct a 90% confidence interval for the mean.

(c) Construct an 80% confidence interval for the mean.

Answer 1

You can use this simple formula .

μ = M ± Z(s_M)

M = sample mean

Z = Z statistic determined by confidence level

s_M = standard error = √(s²/n)

First calculate the average of the sample by adding up the values and dividing by the number of elements in the sample. Then calculate the standard deviation by adding up the squared deviations from the mean.

Because the questions tells you the population is normal you can use a Z table to get the z statistics critical values.

This calculator will give you the result https://www.socscistatistics.com/confidenceinterval/default3.aspx